5) Atvirai bendraudami pamatome ar vienas kitą galim veikti. Dalyvaudami bendroje veikloje mums ima rūpėti jos reikšmė. It is constructive to presume we are directly connected; Each person must have their own reason for communicating.

6) Nuoširdžiai pasižiūrėjęs žinau, ar noriu keistis? I can step back and note the domain of my participation; I change how things look by investing myself in underdefined domains.

7) Aiškiau įsijungiant paaiškėja, kaip apskritai būna (if you are stepped out, then can take a step, but if stepped in, can't take a step); Invest ourselves in one particular piece and step back as a piece in general; Step back from a piece in general and then step in as a piece in particular.

Lottery paradox: There is one winning ticket in a large lottery. It is reasonable to believe of a particular lottery ticket that it is not the winning ticket, since the probability that it is the winner is so very small, but it is not reasonable to believe that no lottery ticket will win.

Ship of Theseus (a.k.a. George Washington's axe or Grandfather's old axe): It seems like you can replace any component of a ship, and it is still the same ship. So you can replace them all, one at a time, and it is still the same ship. However, you can then take all the original pieces, and assemble them into a ship. That, too, is the same ship you began with. - Laivas yra visos dalys ir jų sudėjimas ar dalių visuma ir jos išsivystymas?

Sorites paradox (also known as the paradox of the heap): One grain of sand is not a heap. If you don't have a heap, then adding only one grain of sand won't give you a heap. Then no number of grains of sand will make a heap. Similarly, one hair can't make the difference between being bald and not being bald. But then if you remove one hair at a time, you will never become bald. Also similar, one dollar will not make you rich, so if you keep this up, one dollar at a time, you will never become rich, no matter how much you obtain.

Nontransitive dice: You can have three dice, called A, B, and C, such that A is likely to win in a roll against B, B is likely to win in a roll against C, and C is likely to win in a roll against A.

Grelling–Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? (Another close relative of Russell's paradox.)

Crocodile Dilemma: If a crocodile steals a child and promises its return if the father can correctly guess what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?

Epimenides paradox: A Cretan says: "All Cretans are liars". This paradox works in mainly the same way as the Liar paradox.

Liar paradox: "This sentence is false." This is the canonical self-referential paradox. Also "Is the answer to this question no?" And "I'm lying."

Card paradox: "The next statement is true. The previous statement is false." A variant of the liar paradox that does not use self-reference.

The Pinocchio paradox: What would happen if Pinocchio said "My nose will be growing"?

Quine's paradox: "'Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation." Shows that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals.

Yablo's paradox: An ordered infinite sequence of sentences, each of which says that all following sentences are false. Uses neither self-reference nor circular reference.

[2,3] Buridan's bridge: Will Plato throw Socrates into the water or not?

[1,2] Socratic paradox: "I know that I know nothing at all."

Barber paradox: A male barber shaves all and only those men who do not shave themselves. Does he shave himself? (Russell's popularization of his set theoretic paradox.) Rūšiavimai. Kaimo kirpėjas kerpa būtent visus save neapkerpančius. Ar jis kerpa pats save?

Russell's paradox: Does the set of all those sets that do not contain themselves contain itself?

Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement. Savybių poravimas, jungimas - Jeigu savybės yra išdėstomos kokia nors tvarka, jos gali atrodyti prieštaringai.

Cramer's paradox: the number of points of intersection of two higher-order curves can be greater than the number of arbitrary points needed to define one such curve.

Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached. Išgyvenimo taškas. Ar skaičiuojame įvykį ryšium su priežastimi (monetos kritimu) ar su pasėkme (pabudimu)?

What the Tortoise Said to Achilles "Whatever Logic is good enough to tell me is worth writing down...," also known as Carroll's paradox, not to be confused with the physical paradox of the same name.

Bonini's paradox: models or simulations that explain the workings of complex systems are seemingly impossible to construct: As a model of a complex system becomes more complete, it becomes less understandable; for it to be more understandable it must be less complete and therefore less accurate. When the model becomes accurate, it is just as difficult to understand as the real-world processes it represents.

Exception paradox: "If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception." "There's always an exception to the rule, except to the exception of the rule—which is, in of itself, an accepted exception of the rule."

"If this statement is true, then X" prilygsta "if Not X, then THAT statement is false" arba "if Not X, then THIS statement is false", žiūrint kaip suprasi "this statement". (this ir that primena grue ir bleen).

Bonini's paradox: models or simulations that explain the workings of complex systems are seemingly impossible to construct: As a model of a complex system becomes more complete, it becomes less understandable; for it to be more understandable it must be less complete and therefore less accurate. When the model becomes accurate, it is just as difficult to understand as the real-world processes it represents.

Code-talker paradox: how can a language both enable communication and block communication?

Išskirtinumas ir vidurkis

Išskirtiniai nariai žymiai paveikia vidurkį.

Friendship paradox: For almost everyone, their friends have more friends than they do.

Will Rogers phenomenon: The mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results — for example, it is possible that moving an entry from an encyclopedia to a dictionary would increase the average entry length on both books.

Statistics

Inspection paradox: Why one will wait longer for a bus than one should.

Lindley's paradox: Tiny errors in the null hypothesis are magnified when large data sets are analyzed, leading to false but highly statistically significant results.

Low birth weight paradox: Low birth weight and mothers who smoke contribute to a higher mortality rate. Babies of smokers have lower average birth weight, but low birth weight babies born to smokers have a lower mortality rate than other low birth weight babies. (A special case of Simpson's paradox.)

Probability

The Monty Hall paradox: which door do you choose?

See also: Category:Probability theory paradoxes

Bertrand's box paradox: A paradox of conditional probability closely related to the Boy or Girl paradox.

Necktie Paradox : A wager between two people seems to favour them both. Very similar in essence to the Two-envelope paradox.

Proebsting's paradox: The Kelly criterion is an often optimal strategy for maximizing profit in the long run. Proebsting's paradox apparently shows that the Kelly criterion can lead to ruin.

Simpson's paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.

Three cards problem: When pulling a random card, how do you determine the color of the underside?

Three Prisoners problem: A variation of the Monty Hall problem.

Two-envelope paradox: You are given two indistinguishable envelopes and you are told one contains twice as much money as the other. You may open one envelope, examine its contents, and then, without opening the other, choose which envelope to take.

Infinity and infinitesimals

Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number that is smaller than itself.

Cantor's paradox: There is no greatest cardinal number.

Galileo's paradox: Though most numbers are not squares, there are no more numbers than squares. (See also Cantor's diagonal argument)

Pigeonhole Principle: E.g. there must be at least two people in London with the same number of hairs on their heads

Supertasks can result in paradoxes such as the Ross-Littlewood paradox and Benardete's paradox.

Geometry and topology

The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original.

Banach–Tarski paradox: Cut a ball into a finite number of pieces, re-assemble the pieces to get two balls, both of equal size to the first. The von Neumann paradox is a two-dimensional analogue.

Paradoxical set: A set that can be partitioned into two sets, each of which is equivalent to the original.

Coastline paradox: the perimeter of a landmass is in general ill-defined.

Gabriel's Horn or Torricelli's trumpet: A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals are covered by a finite area, but have an infinite perimeter (in fact, there are no two distinct points on the boundary of the Mandelbrot set that can be reached from one another by moving a finite distance along that boundary, which also implies that in a sense you go no further if you walk "the wrong way" around the set to reach a nearby point). This can be represented by a Klein bottle.

Hausdorff paradox: There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself.

Missing square puzzle: Two similar-looking figures appear to have different areas while built from the same pieces.

Nikodym set: A set contained in and with the same Lebesgue measure as the unit square, yet for every one of its points there is a straight line intersecting the Nikodym set only in that point.

Smale's paradox: A sphere can, topologically, be turned inside out.

Decision theory

Abilene paradox: People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do.

Apportionment paradox: Some systems of apportioning representation can have unintuitive results due to rounding

Alabama paradox: Increasing the total number of seats might shrink one block's seats.

New states paradox: Adding a new state or voting block might increase the number of votes of another.

Population paradox: A fast-growing state can lose votes to a slow-growing state.

Arrow's paradox: Given more than two choices, no system can have all the attributes of an ideal voting system at once.

Buridan's ass: How can a rational choice be made between two outcomes of equal value?

Chainstore paradox: Even those who know better play the so-called chain store game in an irrational manner.

Fenno's paradox: The belief that people generally disapprove of the United States Congress as a whole, but support the Congressman from their own Congressional district.

Green paradox: Policies intending to reduce future CO2 emissions may lead to increased emissions in the present.

Inventor's paradox: It is easier to solve a more general problem that covers the specifics of the sought-after solution.

Kavka's toxin puzzle: Can one intend to drink the non-deadly toxin, if the intention is the only thing needed to get the reward?

Cool tropics paradox: A contradiction between modelled estimates of tropical temperatures during warm, ice-free periods of the Cretaceous and Eocene, and the colder temperatures that proxies suggest were present.

The holographic principle: The amount of information that can be stored in a given volume is not proportional to the volume but to the area that bounds that volume.

Irresistible force paradox: What would happen if an unstoppable force hit an immovable object?

Astrophysics

Algol paradox: In some binaries the partners seem to have different ages, even though they're thought to have formed at the same time.

Faint young Sun paradox: The apparent contradiction between observations of liquid water early in the Earth's history and the astrophysical expectation that the output of the young sun would have been insufficient to melt ice on earth.

The GZK paradox: High-energy cosmic rays have been observed that seem to violate the Greisen-Zatsepin-Kuzmin limit, which is a consequence of special relativity.

Classical mechanics

Archer's paradox: An archer must, in order to hit his target, not aim directly at it, but slightly to the side.

Archimedes paradox: A massive battleship can float in a few litres of water.

Aristotle's wheel paradox: Rolling joined concentric wheels seem to trace the same distance with their circumferences, even though the circumferences are different.

Carroll's paradox: The angular momentum of a stick should be zero, but is not.

D'Alembert's paradox: Flow of an inviscid fluid produces no net force on a solid body.

Denny's paradox: Surface-dwelling arthropods (such as the water strider) should not be able to propel themselves horizontally.

Elevator paradox: Even though hydrometers are used to measure fluid density, a hydrometer will not indicate changes of fluid density caused by changing atmospheric pressure.

Feynman sprinkler: Which way does a sprinkler rotate when submerged in a tank and made to suck in the surrounding fluid?

Painlevé paradox: Rigid-body dynamics with contact and friction is inconsistent.

Tea leaf paradox: When a cup of tea is stirred, the leaves assemble in the center, even though centrifugal force pushes them outward.

Cosmology

Bentley's paradox: In a Newtonian universe, gravitation should pull all matter into a single point.

Fermi paradox: If there are, as probability would suggest, many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious?

Heat death paradox: Since the universe is not infinitely old, it cannot be infinite in extent.

Olbers' paradox: Why is the night sky black if there is an infinity of stars?

Electromagnetism

Faraday paradox: An apparent violation of Faraday's law of electromagnetic induction.

Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics?

Extinction paradox: In the small wavelength limit, the total scattering cross section of an impenetrable sphere is twice its geometrical cross-sectional area (which is the value obtained in classical mechanics).

Hardy's paradox: How can we make inferences about past events that we haven't observed while at the same time acknowledge that the act of observing it affects the reality we are inferring to?

Klein paradox: When the potential of a potential barrier becomes similar to the mass of the impinging particle, it becomes transparent.

Mocanu's velocity composition paradox: a paradox in special relativity.

Supplee's paradox: the buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest.

Trouton-Noble or Right-angle lever paradox. Does a torque arise in static systems when changing frames?

Twin paradox: The theory of relativity predicts that a person making a round trip will return younger than his or her identical twin who stayed at home.

Thermodynamics

Gibbs paradox: In an ideal gas, is entropy an extensive variable?

Loschmidt's paradox: Why is there an inevitable increase in entropy when the laws of physics are invariant under time reversal? The time reversal symmetry of physical laws appears to contradict the second law of thermodynamics.

Maxwell's Demon: The second law of thermodynamics seems to be violated by a cleverly operated trapdoor.

Mpemba paradox: Hot water can, under certain conditions, freeze faster than cold water, even though it must pass the lower temperature on the way to freezing.

Biology

Paradox of enrichment: Increasing the food available to an ecosystem may lead to instability, and even to extinction.

French paradox: the observation that the French suffer a relatively low incidence of coronary heart disease, despite having a diet relatively rich in saturated fats.

Glucose paradox: The large amount of glycogen in the liver cannot be explained by its small glucose absorption.

Gray's Paradox: Despite their relatively small muscle mass, dolphins can swim at high speeds and obtain large accelerations.

Hispanic Paradox: The finding that Hispanics in the U.S. tend to have substantially better health than the average population in spite of what their aggregate socio-economic indicators predict.

Lombard's Paradox: When rising to stand from a sitting or squatting position, both the hamstrings and quadriceps contract at the same time, despite their being antagonists to each other.

Mexican paradox: Mexican children tend to have higher birth weights than can be expected from their socio-economic status.

Paradox of the pesticides: Applying pesticide to a pest may increase the pest's abundance.

Paradox of the plankton: Why are there so many different species of phytoplankton, even though competition for the same resources tends to reduce the number of species?

Peto's paradox: Humans gets cancer with high frequency, while larger mammals, like whales, don’t. If cancer is essentially a negative outcome lottery at the cell level, and larger organisms have more cells, and thus more potentially cancerous cell divisions, you would expect larger organisms to be more predisposed to cancer.

Pulsus paradoxus: Sometimes it is possible to hear, with a stethoscope, heartbeats that can't be felt at the wrist.

Sherman paradox: An anomalous pattern of inheritance in the fragile X syndrome.

Temporal paradox (paleontology): When did the ancestors of birds live?

Levinthal paradox: The length of time that it takes for a protein chain to find its folded state is many orders of magnitude shorter than it would be if it freely searched all possible configurations.

SAR paradox: Exceptions to the principle that a small change in a molecule causes a small change in its chemical behaviour are frequently profound.

Time

Grandfather paradox: You travel back in time and kill your grandfather before he conceives one of your parents, which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather.

Bootstrap paradox: Can a time traveler send himself information with no outside source?

Predestination paradox: A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time. The bootstrap paradox is closely tied to this, in which, as a result of time travel, information or objects appear to have no beginning.

Temporal paradox: What happens when a time traveler does things in the past that prevent him from doing them in the first place?

Philosophy

Paradox of analysis: It seems that no conceptual analysis can both meet the requirement of correctness and of informativeness.

Chicken or the egg: Which came first, the chicken or the egg?

Fitch's paradox: If all truths are knowable, then all truths must in fact be known.

Paradox of free will: If God knew how we will decide when he created us, how can there be free will?

Goodman's paradox: Why can induction be used to confirm that things are "green", but not to confirm that things are "grue"?

Paradox of hedonism: In seeking happiness, one does not find happiness.

Hutton's Paradox: If asking oneself "Am I dreaming?" in a dream proves that one is, what does it prove in waking life?

Lucas paradox: Capital is not flowing from developed countries to developing countries despite the fact that developing countries have lower levels of capital per worker, and therefore higher returns to capital.

Mandeville's paradox: Actions that may be vicious to individuals may benefit society as a whole.

Metzler paradox: The imposition of a tariff on imports may reduce the relative internal price of that good.

Paradox of thrift: If everyone saves more money during times of recession, then aggregate demand will fall and will in turn lower total savings in the population.

Paradox of toil: If everyone tries to work during times of recession, lower wages will reduce prices, leading to more deflationary expectations, leading to further thrift, reducing demand and thereby reducing employment.

Scitovsky paradox: Using the Kaldor–Hicks criterion, an allocation A may be more efficient than allocation B, while at the same time B is more efficient than A.

Service recovery paradox: Successfully fixing a problem with a defective product may lead to higher consumer satisfaction than in the case where no problem occurred at all.

St. Petersburg paradox: People will only offer a modest fee for a reward of infinite expected value.

Perception
For more details on this topic, see Perceptual paradox.

Tritone paradox: An auditory illusion in which a sequentially played pair of Shepard tones is heard as ascending by some people and as descending by others.

Politics

Stability-instability paradox: When two countries each have nuclear weapons, the probability of a direct war between them greatly decreases, but the probability of minor or indirect conflicts between them increases.

History

Georg Wilhelm Friedrich Hegel: We learn from history that we do not learn from history. (paraphrased)